In this note, we prove that on a surface with Alexandrov’s curvature bounded below, the distance derives from a Riemannian metric whose components, for any p ∈ [1, 2), locally belong to W1,p out of a discrete singular set. This result is based on Reshetnyak’s work on the more general class of surfaces with bounded integral curvature.
@article{bwmeta1.element.doi-10_1515_agms-2016-0012,
author = {Luigi Ambrosio and J\'er\^ome Bertrand},
title = {On the Regularity of Alexandrov Surfaces with Curvature Bounded Below},
journal = {Analysis and Geometry in Metric Spaces},
volume = {4},
year = {2016},
zbl = {1353.53018},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0012}
}
Luigi Ambrosio; Jérôme Bertrand. On the Regularity of Alexandrov Surfaces with Curvature Bounded Below. Analysis and Geometry in Metric Spaces, Tome 4 (2016) . http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_1515_agms-2016-0012/